The linear-in-frequency relaxation rate with a slope close to unity is a dependence reminiscent of strongly correlated metals
that exhibit the marginal Fermi liquid phenomenology
The low-frequency excitations above the localized state are resonant particle–hole excitations, in which a particle is moved between two
nearby localized orbitals. These excitations are local electric dipoles, and thus naturally interact via 1/R3
dipole–dipole interactions
A dipolar excitation can coherently hop on this network, at a rate one can calculate (Supplementary Section IV) to be ~ω.
The analysis of the previous section shows how a combination of Coulomb blockade and dipolar hopping can give rise to the experimentally observed Γ(ω) ∼ ω for the relaxation of a TLS in an electron glass. The prefactor
(ignoring logarithms) is $ξ^3 (V/W)^2$, which is not necessarily small, if the typical microscopic hopping amplitude between
adjacent P sites is comparable to the Coulomb interaction between them. This framework also naturally reproduces
the sharpening of the TLS frequency as one increases the temperature up to T ' ω: when delocalization takes place
through coherent tunneling at zero temperature, the finite-temperature corrections usually suppress transport through
decoherence
Within our zero-temperature theory the processes responsible for T1 and T2 are the same, so we expect these
quantities to be related by some simple scale factor; this is indeed what we observe. However, the trends with
increasing temperature are different: T1 grows with temperature, while T2 remains roughly constant (so the ratio T1/T2
increases). A natural interpretation is that this approximate temperature-independence comes from a competition
between the increasing T1 time and the opening of thermal dephasing channels
Acknowledgements
We thank A. Burin, Y. Galperin, Y.-B. Kim, A. Legros, I. Martin, A. Millis, V. Oganesyan,
S. Paramesweran, B. Shklovskii and Y. Yuan for helpful discussions.
In such a system, the Fermi energy EF lies below a mobility edge Ec that separates localized electronic states from extended states. The free electron density of states is then replaced by a quasiparticle density of states, but the expressions for the Sommerfeld constant and the Pauli-paramagnetic susceptibility of the system remain formally the same [25]. Very often EF can be tuned by changing the charge-carrier concentration to transform an insulating Fermi glass (EF < Ec) to a metal (EF > Ec)
## 2021 [Observation of a marginal Fermi glass](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5445/mahmood2021.pdf)
> **The linear-in-frequency relaxation rate with a slope close to unity** is a dependence reminiscent of strongly correlated metals
> that exhibit the marginal Fermi liquid phenomenology
> The low-frequency excitations above the localized state are resonant particle–hole excitations, in which a particle is moved between two
> nearby localized orbitals. These excitations are local electric dipoles, and thus naturally interact via 1/R3
> dipole–dipole interactions
> **A dipolar excitation can coherently hop on this network**, at a rate one can calculate (Supplementary Section IV) to be ~ω.
[supplements](https://static-content.springer.com/esm/art%3A10.1038%2Fs41567-020-01149-0/MediaObjects/41567_2020_1149_MOESM1_ESM.pdf)
> The analysis of the previous section shows how a combination of Coulomb blockade and dipolar hopping can
> **give rise to the experimentally observed Γ(ω) ∼ ω for the relaxation of a TLS in an electron glass**. The prefactor
> (ignoring logarithms) is $ξ^3 (V/W)^2$, which is not necessarily small, if the typical microscopic hopping amplitude between
> adjacent P sites is comparable to the Coulomb interaction between them. This framework also naturally reproduces
> the sharpening of the TLS frequency as one increases the temperature up to T ' ω: when delocalization takes place
> through coherent tunneling at zero temperature, the finite-temperature corrections usually suppress transport through
> decoherence
> Within our zero-temperature theory the processes responsible for T1 and T2 are the same, so we expect these
> quantities to be related by some simple scale factor; this is indeed what we observe. However, the trends with
> increasing temperature are different: **T1 grows with temperature, while T2 remains roughly constant** (so the ratio T1/T2
> increases). A natural interpretation is that this approximate temperature-independence comes from a competition
> between the increasing T1 time and the opening of thermal dephasing channels
Acknowledgements
We thank **A. Burin, Y. Galperin,** Y.-B. Kim, A. Legros, **I. Martin, A. Millis, V. Oganesyan,**
S. Paramesweran, B. Shklovskii and Y. Yuan for helpful discussions.
[Recent advances in spectroscopy give access to the decay time of excitations in disordered insulating silicon close to the metal–insulator transition, revealing similarities to high-temperature cuprate superconductors](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5449/miranda2021.pdf)
- popular news
https://physics.illinois.edu/news/34879
https://phys.org/news/2021-02-marginal-fermi-glass.html
## 2008? [LaBaNiO4: A Fermi glass](https://arxiv.org/ftp/arxiv/papers/0809/0809.2329.pdf)
> In such a system, **the Fermi energy EF lies below a mobility edge Ec that separates localized electronic states from extended states**. The free electron density of states is then replaced by a quasiparticle density of states, but the expressions for the Sommerfeld constant and the Pauli-paramagnetic susceptibility of the system remain formally the same [25]. Very often EF can be tuned by changing the charge-carrier concentration to transform an insulating Fermi glass (EF < Ec) to a metal (EF > Ec)
https://iopscience.iop.org/article/10.1088/0953-8984/21/1/015701
## [Fermi glass carrier relaxation through the Anderson transition in YBa2Cu3O7−δ investigated by ultrafast Raman scattering](https://arxiv.org/pdf/cond-mat/9705287.pdf) D.Mihailovic, I.Poberaj
> A study of photoexcited carrier relaxation in YBa2Cu3O7−δ by picosecond resonant Raman spectroscopy
